## proving inequality involving limits

Let $(a_{n} ; n\ge 1)$,
$(b_{n}; n\ge 1)$ and
$(l_{n}; n\ge 1)$
be three sequences of real numbers. Supose that
$l_{n} \in [0,1]$
for every n, and let
$c_{n}=l_{n}a_{n}+(1-l_{n})b_{n}$.
Assuming that
$lim sup a_{n}$ and
$lim sup b_{n}$ are finite, please
prove the following inequality:

$lim sup c_{n} \le max(lim sup a_{n},lim sup b_{n})$